-x+3/4=-x^2+2x+3 eching

$$- x + \frac { 3 } { 4 } = - x ^ { 2 } + 2 x + 3$$

x uchun yechish

$$x = \frac{3 \sqrt{2} + 3}{2} \approx 3,621320344$$

$$x=\frac{3-3\sqrt{2}}{2}\approx -0,621320344$$

Kvadrat tenglamalaridan foydalanish qoidalari

x^{2} ni ikki tarafga qo’shing.

$$-x+\frac{3}{4}+x^{2}=2x+3$$

Ikkala tarafdan 2x ni ayirish.

$$-x+\frac{3}{4}+x^{2}-2x=3$$

Ikkala tarafdan 3 ni ayirish.

$$-x+\frac{3}{4}+x^{2}-2x-3=0$$

-\frac{9}{4} olish uchun \frac{3}{4} dan 3 ni ayirish.

$$-x-\frac{9}{4}+x^{2}-2x=0$$

-3x ni olish uchun -x va -2x ni birlashtirish.

$$-3x-\frac{9}{4}+x^{2}=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x^{2}-3x-\frac{9}{4}=0$$

Ushbu tenglama standart shaklidadir: ax^{2}+bx+c=0. Kvadrat tenglama formulasida, \frac{-b±\sqrt{b^{2}-4ac}}{2a} 1 ni a, -3 ni b va -\frac{9}{4} ni c bilan almashtiring.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\left(-\frac{9}{4}\right)}}{2}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\left(-\frac{9}{4}\right)}}{2}$$

-4 ni -\frac{9}{4} marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+9}}{2}$$

9 ni 9 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{18}}{2}$$

18 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±3\sqrt{2}}{2}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±3\sqrt{2}}{2}$$

x=\frac{3±3\sqrt{2}}{2} tenglamasini yeching, bunda ± musbat. 3 ni 3\sqrt{2} ga qo'shish.

$$x=\frac{3\sqrt{2}+3}{2}$$

x=\frac{3±3\sqrt{2}}{2} tenglamasini yeching, bunda ± manfiy. 3 dan 3\sqrt{2} ni ayirish.

$$x=\frac{3-3\sqrt{2}}{2}$$

Tenglama yechildi.

$$x=\frac{3\sqrt{2}+3}{2} x=\frac{3-3\sqrt{2}}{2}$$

Kvadratni yakunlash bo'yicha qadamlar

x^{2} ni ikki tarafga qo’shing.

$$-x+\frac{3}{4}+x^{2}=2x+3$$

Ikkala tarafdan 2x ni ayirish.

$$-x+\frac{3}{4}+x^{2}-2x=3$$

Ikkala tarafdan \frac{3}{4} ni ayirish.

$$-x+x^{2}-2x=3-\frac{3}{4}$$

\frac{9}{4} olish uchun 3 dan \frac{3}{4} ni ayirish.

$$-x+x^{2}-2x=\frac{9}{4}$$

-3x ni olish uchun -x va -2x ni birlashtirish.

$$-3x+x^{2}=\frac{9}{4}$$

Bu kabi kvadrat tenglamalarni kvadratni yakunlab yechish mumkin. Kvadratni yechish uchun tenglama avval ushbu shaklda bo'lishi shart: x^{2}+bx=c.

$$x^{2}-3x=\frac{9}{4}$$

-3 ni bo‘lish, x shartining koeffitsienti, 2 ga -\frac{3}{2} olish uchun. Keyin, -\frac{3}{2} ning kvadratini tenglamaning ikkala tarafiga qo‘shing. Ushbu qadam tenglamaning chap qismini mukammal kvadrat sifatida hosil qiladi.

$$x^{2}-3x+\left(-\frac{3}{2}\right)^{2}=\frac{9}{4}+\left(-\frac{3}{2}\right)^{2}$$

Kasrning ham suratini, ham maxrajini kvadratga ko'paytirib -\frac{3}{2} kvadratini chiqarish.

$$x^{2}-3x+\frac{9}{4}=\frac{9+9}{4}$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{9}{4} ni \frac{9}{4} ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$x^{2}-3x+\frac{9}{4}=\frac{9}{2}$$

x^{2}-3x+\frac{9}{4} omili. Odatda, x^{2}+bx+c mukammal kvadrat bo'lsa, u doimo \left(x+\frac{b}{2}\right)^{2} omil sifatida bo'lishi mumkin.

$$\left(x-\frac{3}{2}\right)^{2}=\frac{9}{2}$$

Tenglamaning ikkala tarafining kvadrat ildizini chiqarish.

$$\sqrt{\left(x-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{2}}$$

Qisqartirish.

$$x-\frac{3}{2}=\frac{3\sqrt{2}}{2} x-\frac{3}{2}=-\frac{3\sqrt{2}}{2}$$

\frac{3}{2} ni tenglamaning ikkala tarafiga qo'shish.

$$x=\frac{3\sqrt{2}+3}{2} x=\frac{3-3\sqrt{2}}{2}$$